init

README.md

@@ -1,7 +1,7 @@
 ---
 title: Percolation
-emoji: 😻
-colorFrom: gray
+emoji: 🧱
+colorFrom: blue
 colorTo: gray
 sdk: gradio
 sdk_version: 5.6.0

app.py

@@ -0,0 +1,133 @@
+import gradio as gr
+import numpy as np
+import matplotlib.pyplot as plt
+import time
+from scipy.ndimage import label
+
+
+def create_initial_plot(grid_size):
+    grid = np.zeros((grid_size, grid_size))
+    fig = plt.figure(figsize=(15, 6))
+    grid_ax = fig.add_subplot(121)
+    graph_ax = fig.add_subplot(122)
+
+    grid_ax.imshow(grid, cmap='Greys', alpha=0.3)
+    grid_ax.set_title(
+        f'Site Occupation Probability p = 0.00\n'
+        f'Largest Cluster Ratio = 0.000'
+    )
+
+    graph_ax.plot([0], [0], '-b', label='Largest Cluster Size')
+    graph_ax.set_xlabel('Occupation Probability p')
+    graph_ax.set_ylabel('Largest Cluster Size Ratio')
+    graph_ax.set_title('Phase Transition in 2D Percolation')
+    graph_ax.grid(True)
+    graph_ax.legend()
+    graph_ax.set_xlim(0, 1)
+    graph_ax.set_ylim(0, 1)
+
+    plt.tight_layout()
+    return fig
+
+def get_largest_cluster(grid):
+    labeled_array, num_features = label(grid)
+    if num_features == 0:
+        return np.zeros_like(grid), 0
+
+    sizes = [np.sum(labeled_array == i) for i in range(1, num_features + 1)]
+    if not sizes:
+        return np.zeros_like(grid), 0
+
+    max_cluster_index = np.argmax(sizes) + 1
+    max_cluster_mask = labeled_array == max_cluster_index
+    max_cluster_size = sizes[max_cluster_index - 1]
+
+    return max_cluster_mask, max_cluster_size
+
+def run_percolation_simulation(grid_size):
+    p_step = 0.02
+    fine_step = 0.01
+
+    p1 = np.arange(0, 0.56, p_step)
+    p2 = np.arange(0.56, 0.60 + fine_step, fine_step)
+    p3 = np.arange(0.60 + p_step, 1.0 + p_step, p_step)
+    steps = np.concatenate((p1, p2, p3))
+
+    p_values = []
+    largest_clusters = []
+
+    fig = plt.figure(figsize=(15, 6))
+    grid_ax = fig.add_subplot(121)
+    graph_ax = fig.add_subplot(122)
+
+    np.random.seed(3407)
+    for p in steps:
+        grid = np.random.random((grid_size, grid_size)) < p
+        largest_cluster_mask, largest_cluster_size = get_largest_cluster(grid)
+        largest_cluster_ratio = largest_cluster_size / (grid_size * grid_size)
+
+        p_values.append(p)
+        largest_clusters.append(largest_cluster_ratio)
+
+        grid_ax.clear()
+        graph_ax.clear()
+
+        grid_ax.imshow(grid, cmap='Greys', alpha=0.3)
+        grid_ax.imshow(largest_cluster_mask, cmap='Blues', alpha=0.7)
+
+        grid_ax.set_title(
+            f'Site Occupation Probability p = {p:.2f}\n'
+            f'Largest Cluster Ratio = {largest_cluster_ratio:.3f}'
+        )
+
+        graph_ax.plot(p_values, largest_clusters, '-b', label='Largest Cluster Size')
+        graph_ax.set_xlabel('Occupation Probability p')
+        graph_ax.set_ylabel('Largest Cluster Size Ratio')
+        graph_ax.set_title('Phase Transition in 2D Percolation')
+        graph_ax.grid(True)
+        graph_ax.legend()
+        graph_ax.set_xlim(0, 1)
+        graph_ax.set_ylim(0, 1)
+
+        plt.tight_layout()
+
+        yield fig
+
+        time.sleep(0.25)
+
+with gr.Blocks() as demo:
+    gr.Markdown("# 2D Site Percolation Simulation")
+    gr.Markdown("""
+    This simulation shows the formation of clusters in a 2D percolation system as the occupation probability increases.
+    Watch how the system undergoes a phase transition around p ≈ 0.593 (critical point).
+
+    - Gray dots: Occupied sites
+    - Blue region: Largest connected cluster
+    """)
+
+    with gr.Row():
+        plot = gr.Plot(value=create_initial_plot(50))
+    with gr.Row():
+        grid_size = gr.Slider(
+            minimum=20, maximum=200, step=10, value=150,
+            label="Grid Size", info="Size of the simulation grid"
+        )
+    with gr.Row():
+        start_btn = gr.Button("Start Simulation")
+
+    start_btn.click(
+        fn=run_percolation_simulation,
+        inputs=[grid_size],
+        outputs=plot,
+        show_progress=False
+    )
+    grid_size.change(
+        fn=create_initial_plot,
+        inputs=[grid_size],
+        outputs=plot
+    )
+
+if __name__ == "__main__":
+    demo.queue().launch(
+        debug=True
+    )

requirements.txt

@@ -0,0 +1,3 @@
+matplotlib==3.8.0
+numpy==1.26.4
+scipy==1.13.1